Nuprl Lemma : subtype_rel-random-variable
∀[k:FinProbSpace]. ∀[n,m:ℕ]. RandomVariable(k;n) ⊆r RandomVariable(k;m) supposing n ≤ m
Proof
Definitions occuring in Statement :
random-variable: RandomVariable(p;n),
finite-prob-space: FinProbSpace,
nat: ℕ,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
le: A ≤ B
Definitions unfolded in proof :
random-variable: RandomVariable(p;n),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
nat: ℕ,
finite-prob-space: FinProbSpace,
so_lambda: λ2x.t[x],
so_apply: x[s],
and: P ∧ Q,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B
Lemmas referenced :
subtype_rel_dep_function,
int_seg_wf,
length_wf,
rationals_wf,
int_seg_subtype,
false_wf,
subtype_rel_self,
le_wf,
nat_wf,
finite-prob-space_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
lambdaEquality,
independent_isectElimination,
because_Cache,
independent_pairFormation,
lambdaFormation,
axiomEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[k:FinProbSpace]. \mforall{}[n,m:\mBbbN{}]. RandomVariable(k;n) \msubseteq{}r RandomVariable(k;m) supposing n \mleq{} m
Date html generated:
2016_05_15-PM-11_46_03
Last ObjectModification:
2015_12_28-PM-07_16_29
Theory : randomness
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